Induced emf:

$\overline{){\mathbf{\epsilon}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{d}{\mathbf{\varphi}}_{\mathbf{B}}}{\mathbf{d}\mathbf{t}}}$

Power rule of derivation,

$\overline{)\frac{\mathit{d}}{\mathit{d}\mathit{t}}\mathbf{\left(}{\mathit{t}}^{\mathit{n}}\mathbf{\right)}{\mathbf{=}}{\mathit{n}}{{\mathit{t}}}^{\mathit{n}\mathbf{-}\mathbf{1}}}$

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{B}}}{\mathbf{=}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}{\mathbf{\xb7}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{A}}}$

B = (0.31t i + 0.55t^{2} k)T

A = (0.17 m × 0.17 m) k = (0.0289 m^{2}) k (The area is perpendicular to the z-plane

${{\mathbf{\varphi}}}_{{\mathbf{B}}}$= (0.31t i + 0.55t^{2} k)•(0.0289 m^{2}) k = (0.55t^{2} k)•(0.0289) k = **0.015895t ^{2} T•m**

1)

A (17cm × 17cm) square loop lies in the xy plane. The magnetic field in this region of space is B = (0.31t î + 0.55t^{2} k̂)T where t is in seconds.

1) What is the induced emf in the loop at 0.5 s?

2) What is the induced emf in the loop at 1.0 s?

Express your answer to two significant figures and include the appropriate units.

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